Birthday paradox

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Birthday paradox

How likely a shared birthday is, and how fast that rises.

It runs entirely in this browser tab: what you type is never uploaded, and the tool makes no network request while it works. Open your browser's network panel and try it — nothing leaves the page. There is no sign-up and no account.

Settings

The table of counts
Every group size up to the one asked for, which is the only way to see how fast the curve rises.

How to use it

  1. Paste your text into the box above, or open a file.
  2. Adjust the settings beside it until the result is what you wanted.
  3. Copy the result, or save it as a file. The result updates as you type.

Questions

Why does this disagree with my spreadsheet?
Usually because one of you is using a different definition, and the tool says which one it used. A percentile has six in ordinary use, a standard deviation has two divisors, and a histogram's class count is a rule with a name. Where the choice moves the answer it is a setting here.
Does a p-value below 0.05 mean the result is true?
No. A p-value is the probability of seeing data at least this extreme if there were no real difference. It is not the probability that there is none, and a difference can be distinguishable from noise and far too small to matter.
How exact are the distributions?
They are series and continued fractions stopped when a term stops changing the answer, and searches bisected to a stated tolerance — right to more places than anybody reports a p-value to. Where one does not settle, the result says so rather than showing where it stopped as though it were the answer.
Is what I type uploaded anywhere?
No. This page carries the whole tool as WebAssembly and runs it on your own device. Nothing you type is sent anywhere, and there is no network request to make while it works.

Other tools for probability

Dice probability
The whole distribution of a total, counted rather than simulated.

Lottery odds
The chance of matching a draw, at every prize tier.

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